I have created a custom list (Department Contact List) in SharePoint which will be added as a webpart to different pages. So the list shows only the information relating to the page it is on. I have modified the view of the webpart. However, when I save the page the List Name (Department Contact List) has become a hyperlink. Is there any way to stop this from happening? Not only does it not look great but It may confuse people.
Unfortunately, there's no way that I know of to simply remove the link. You can modify the link, or you can remove the title completely.
To modify the link, edit the page, and get to the web part properties. From there, go to Advanced --> Title URL, and change it as desired. If you simply delete whatever is there, I believe that SP just resets it to the default, so perhaps change it to the URL of the page it's on, or any other more appropriate URL.
To remove the title completely, and get to the web part properties. From there, go to Appearance, and change "Chrome Type" to "None". A common hack people do with this is they add text right above the web part to act as a title. Depending on the version of SP you're using and which page layout is in use, you can either type text directly above the web part, or you can add a content editor web part right above the list web part.
If what you are talking about is the webpart's title taking people to the custom list, the only way I have effectively addressed that is to change the Chrome for the webpart's appearance setting from "Default" to None or Border only and then adding a content editor webpart above it and type in and format the title I want.